Question:
With reference to \(Z = \frac{1+2i}{1-(1-i)^2}\), what is the principal argument of \(Z\)?
\(Z = \frac{1+2i}{1-(1-i)^2}\) के संदर्भ में, \(Z\) का मुख्य कोणांक (argument) क्या है?
Options:
- 0
- \(\pi/4\)
- \(\pi/2\)
- \(\pi\)
- 0
- \(\pi/4\)
- \(\pi/2\)
- \(\pi\)
Correct Answer: a)
Explanation:
From the previous question, \(Z = 1 = 1 + 0i\).
Since \(Z\) is a strictly positive real number lying on the positive real axis:
\[\arg(Z) = \tan^{-1}\left(\frac{0}{1}\right) = 0\]
Hence, the correct option is (a).
पिछले प्रश्न से, \(Z = 1 = 1 + 0i\)।
चूँकि \(Z\) धनात्मक वास्तविक अक्ष पर स्थित एक वास्तविक संख्या है:
\[\arg(Z) = 0\]
अतः सही विकल्प (a) है।